We present a theoretical framework for the generation and scattering of second-harmonic and sum-frequency light from the surface of particles of arbitrary shape in the limit of low index of refraction contrast. For homogeneous and isotropic surfaces, light scattering can be described by a finite set of scattering functions. Selection rules regarding these scattering functions are presented. We also find that the scattering functions associated with achiral and chiral surfaces are directly related to the bulk and surface linear optical form factors, respectively. Finally, we derive explicit expressions for particles of ellipsoidal shape, for which we calculate angular scattering patterns as a function of particle orientation and for ensembles of particles. (C) 2011 Optical Society of America